Let n be the smallest composite number such that it can be written as the product of two positive integers that differ by 10. How many distinct prime factors does n have?

Question

Mathematics

Hebert

4 May, 04:36

Let n be the smallest composite number such that it can be written as the product of two positive integers that differ by 10. How many distinct prime factors does n have?

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Answers (1)

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Ayaan Warner · Answer 1

Answer: n has two distinct prime factors 2 and 3.

Step-by-step explanation:

As given the smallest composite number such that it can be written as the product of two positive integers that differ by 10.

i. e. if first number be x then the other number be x+10 and n=x (x+10), where n must be composite number.

So after putting the values of x by positive integer

1) x=0 then n=0 (10+0) = 0 ... which is not a composite number.

2) x=1 then n=1 (1+10) = 11 ... which is not a composite number.

3) x=2 then n=2 (2+10) = 24 ... which is a composite number.

so our n=24 and we know that 24=2*2*2*3

Therefore its distinct prime factors are 2 and 3.